Abstract
We investigate whether a color-sextet scalar diquark (${\bf H}_6$) coupling to the left-handed quarks contributes to the $\Delta S=2$ process. It is found that the box diagrams mediated by $W$ and ${\bf H}_6$ bosons have no contributions to $\Delta S=2$ when the limit of $m_t=0$ is used, and the flavor mixing matrices for diagonalizing quark mass matrices are introduced at the same time. When the heavy top-quark mass effects are taken into account, it is found that in addition to the $W-{\bf H}_6$ box diagrams significantly contributing to $\Delta S=2$, their effects can be as large as those from the ${\bf H}_6-{\bf H}_6$ box diagrams. Using the parameters that are constrained by the $K^0-\bar K^0$ mixing parameter $\Delta M_K$ and the Kaon indirect CP violation $\epsilon_K$, we find that the left-handed color-sextet diquark can lead to the Kaon direct CP violation being $Re(\epsilon'/\epsilon) \sim 0.4 \times 10^{-3}$. In the chosen scheme, although the diquark contribution to $K_L\to \pi^0 \nu \bar\nu$ is small, the branching ratio of $K^+ \to \pi^+ \nu \bar\nu$ can reach the current experimental upper bound.
Highlights
Despite the success of the standard model (SM) in explaining most experimental data, the SM is an effective theory only at the electroweak (EW) scale because some long-standing phenomena are still puzzling, such as baryogenesis, neutrino mass, and the muon anomalous magnetic dipole moment
It is found that the box diagrams mediated by W and H6 bosons have no contributions to ΔS 1⁄4 2 when the limit of mt 1⁄4 0 is used, and the flavor mixing matrices for diagonalizing quark mass matrices are introduced at the same time
Using the parameters that are constrained by the K0 − K 0 mixing parameter ΔMK and the kaon indirect CP violation εK, we find that the left-handed color-sextet diquark can lead to the kaon direct CP violation being Reðε0=εÞ ∼ 0.3 × 10−3
Summary
Despite the success of the standard model (SM) in explaining most experimental data, the SM is an effective theory only at the electroweak (EW) scale because some long-standing phenomena are still puzzling, such as baryogenesis, neutrino mass, and the muon anomalous magnetic dipole moment. It can be verified that before EW symmetry breaking (EWSB), the Yukawa couplings of H3 1⁄4 ð3; 1; −1=3Þ and H6 1⁄4 ð6; 1; 1=3Þ to the left-handed quark doublets are flavor symmetric and antisymmetric, respectively. The antisymmetric H6 Yukawa matrix only has three independent elements; if we assume that the new Yukawa couplings are real parameters, there are only four new parameters involved, including the diquark mass. In addition to involving fewer parameters, H6 has some interesting characteristics It was argued in [7] that the box diagrams mediated by one W gauge boson and one H6 for ΔS 1⁄4 2 vanish. In order to study the color-sextet diquark effects, we introduce the diquark Yukawa couplings to the SM quarks and its gauge couplings to the EW gauge bosons. With the real diquark Yukawa matrix, the loop contributions to ε0=ε and K → πννare dominated by the Z-penguin [9], so we skip discussions of the diquark coupling to the gluons
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